Plane Distance

Why

What is the distance between two points in a plane?

Definition

We define the distance between two points in the plane as the length of the line segment connecting them.¹ In terms of their coordinates $(x_1, x_2), (y_1, y_2) \in \R ^2$, the plane distance of two points is

\[ \sqrt{(x_1 - y_1)^2 + (x_2 - y_2)^2}. \]

This is sometimes referred to as the Euclidean distance. We have thus defined a function mapping $\R ^2 \times \R ^2$ into $\R $.

This intuition will be expanded in future editions. ↩︎